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Applications of the Euler characteristic

Simon Donaldson

in Riemann Surfaces

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198526391
eISBN:
9780191774874
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526391.003.0007
Subject:
Mathematics, Geometry / Topology, Analysis

The genus of a compact oriented smooth surface S can be defined as one-half the dimension of the de Rham cohomology group H 1(S). Another way of defining the genus involves the ... More


From classical to modern

Dusa McDuff and Dietmar Salamon

in Introduction to Symplectic Topology

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198794899
eISBN:
9780191836411
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198794899.003.0002
Subject:
Mathematics, Analysis, Geometry / Topology

The first chapter develops the basic concepts of symplectic topology from the vantage point of classical mechanics. It starts with an introduction to the Euler–Lagrange equation and shows how the ... More


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